Chief executive Alex Cruz said Heathrow's queues were "significantly worse" than elsewhere in the continent.
He added tackling lengthy queues should be a priority for the Government rather than a reported idea of designated lanes for UK passport holders post-Brexit.
Writing in the Times, Mr Cruz said: "Two-hour queues are fast becoming the norm for those visiting from outside the European Economic Area (EEA), despite a target of no more than a 45-minute wait.
"Even EEA citizens wait almost an hour. This is unacceptable, yet Nick Jariwalla, the head of Border Force at Heathrow, said recently that things were unlikely to change and it was unreasonable for his team to be expected to meet their targets."
Mr Cruz, who succeeded Keith Williams as CEO in April 2016, said the airport has missed its target for non-EEA arrivals more than 6,000 times this year.
Official figures show that the country's Border Force at Heathrow missed their waiting-time targets more than 100 times in one day last December.
He wrote: "Queues are significantly worse than at many other major world airports. What kind of message does this send, as we try to build links outside the EU?"
A number of arriving passengers at Terminal 4 were forced to wait three hours before being processed owing to "lack of staffing" during England's second-round game against Colombia on July 3.
With only 11 out of 28 staff at their posts, a Heathrow boss was forced to warn that immigration desks should not be abandoned by border officials again when England played in the World Cup semi-final.
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Passport queues have been getting so bad that passengers are being forced to wait on the tarmac after landing.
A Home Office spokesman said: "The vast majority of people who arrive at Heathrow get through the border within our service standards.
"But we understand the frustration for those who have experienced longer waits and remain fully committed to working with our partners to reduce waiting times as far as is possible.
"At the same time, we will not compromise the essential checks we carry out at the border which keep our country safe.
"We are making sure Border Force has the resources it needs and are deploying 200 additional staff at Heathrow over the summer."
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